Noise estimation is required in many algorithms to process images or video optimally. For example, in TV systems, noise reduction is often applied as a first step to obtain noise-free video sequences. An optimal algorithm of noise reduction is noise adaptive, which first estimates the noise variance of input video sequences, and then performs noise reduction. Noise estimation is very important in this case, because overestimation leads to image blurring and underestimation leads to insufficient noise reduction. The input image g is generally assumed to be corrupted by additive Gaussian noise N(0, σ20):g=f+n  (1)
where f is the original noise-free image and the noise n˜N(0, σ20). For each pixel:gij=fij+nij  (2)
where (i, j) is the coordinate of each pixel, gij, and fij denote the pixel values in image g and f, and nij˜N(0, σ20). The problem of noise estimation is to estimate the noise variance σ20 of the contaminated image g without the priori information of the original image f.
A straightforward method of noise estimation is to compute the expectation of the local variance of image g. This method suffers from the image structure which causes overestimation. To overcome this problem, several methods have been proposed. One method excludes the local variance if the gradient magnitude of the corresponding pixel is greater than a preset threshold. However, the gradient magnitude is also related to noise variance, so it is hard to find an appropriate threshold. Another method, first extracts the noise component with little structure by applying high-pass filters to the contaminated image g, and then performs noise estimation on the noise component. Another method decomposes the image into a pyramid structure of different block sizes. The noise variance is estimated from a sequence of four smallest block-based local variance at each level. Yet in another method, Reyleigh distribution is fitted to the magnitude of the intensity gradient. The noise variance is estimated based on the attribute that the Rayleigh probability density function reaches maximum at value σ0. Other methods estimate multiplicative as well as additive noise. Overall, all of the above methods utilize the spatial local statistics to estimate noise variance. However, estimation accuracy depends on the separation of the noise component and the real image signal. The robustness degrades greatly if most of the image contains complicated structure.